My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

These practical challenges are all about making a 'tray' and covering it with paper.

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Can you find out in which order the children are standing in this line?

What two-digit numbers can you make with these two dice? What can't you make?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

What could the half time scores have been in these Olympic hockey matches?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

My coat has three buttons. How many ways can you find to do up all the buttons?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

What happens when you try and fit the triomino pieces into these two grids?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

This challenge is about finding the difference between numbers which have the same tens digit.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?